Advertisements
Advertisements
Question
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Advertisements
Solution
`cos^2 26^@ + cos 64^@ sin 26^@ + tan 36^@/cot 54^@`
`= cos^2 26^@ + cos(90^@ - 26^@) sin 26^@ + tan 36^@/(cot(90^@ - 36^@))`
`= cos^2 26^@ + sin 26^@.sin26^@ + tan36^@/tan36^@` `[∵ cos(90^@ - theta) = sin theta, cot(90^@ - theta) = tan theta]`
`= cos^2 26^@ + sin^2 26^@ + 1`
`= 1 + 1 [∵ cos^2 theta + sin^2 theta = 1]`
= 2
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
